As you can see from Craig’s notes the discussion is wide-ranging; so well worth a listen, this will leave you with plenty to think about.

I was particularly struck by Anne and John’s Big 3 (or Big 5!) (scroll down Craig’s notes). The only website they mentioned is Underground Maths; a personal favourite – Underground Maths pages here). John Holt’s How Children Learn was my first reading on my teacher training course decades ago – still a classic.

This morning, I have been distracted from writing watching Anne and John’s recommendation – Polya’s video “Let us teach guessing”. (Also on YouTube). To hear the man himself talking to his class is a joy. Not a traditional lecture – join in with his class as they guess!

Much food for thought – you can hear Polya’s summary of what is important in reasonable guessing at 54:16. Including the all-important reminder that we must test our guesses.

From the University of California, Berkeley see this summary of Polya’s problem-solving techniques – including a summary, in the Polya’s own words, on strategies for attacking problems in mathematics class from the book, How To Solve It, by George Polya, 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6.

Exam Board specific GCSE content is available, my Year 10 students have tried this and reacted very favourably; this is certainly something I will be using with my students in the coming academic year; the step by step explanations and examples look very helpful indeed. My students certainly liked the AQA GCSE Maths sections we looked at – they also strayed into the many other subjects available, liking the content they saw.

Happily, Seneca has just announced that KS3 and A Level courses will also be free – such excellent news.

A new simulation in the excellent HTML5 collection – from PhET Interactive Simulations, we have Area Model Algebra, this is very simple to use. Rectangles of various sizes can be built showing the relationship between multiplication and area.

As we come to the end of an academic year and look to a new one, it will be a time of change for many students. Perhaps you have completed GCSEs or equivalent qualifications (UK age 15-16) and are about to start on your A Levels or perhaps you have completed those and are about to start studying Mathematics at university.

To be in a position to begin your new courses well you should be thoroughly familiar with the essentials of the work you have studied to date. At whichever level you are studying your Algebra should be at a standard where you can manipulate expressions with ease.

Some resources to help you prepare and will be useful reference material for you during your course…

OCR – Bridging the Gap – A Student Guide

For students going on to A Level then the best thing you could do is use…